Hi I currently play on Xbox Series x and have done for the last 6 months but before that I was on ps4. The app shows my characters and how high I have got them on my xbox as if they was on my ps4 but only shows one 1100 on my xbox system when u change the drop down menu. I'm trying to pull a cloak out of last seasons pass but keeps saying failed as inventory full but I have spaces in my cloak slot.
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Cross-save allows you to access the data from your active account, PSN in your case, across all of your linked platforms. The data does not transfer to the other accounts, and it will always be permanently tied to your PSN account. It is correct that your Xbox account will show as having no recent progress on those characters, as you are using your PSN data to play the game. Regardless of what platform you are playing on, the save data is in fact PSN data. You need to be looking at your PSN data whenever you use the companion app, the Bungie website, or third party sites. It is your PSN data that you are playing the game with, not your Xbox data.